Bài giảng Operations Management - Module C: Transportation Models

Operations ManagementTransportation ModelsModule C1OutlineTRANSPORTATION MODELINGDEVELOPING AN INITIAL SOLUTIONThe Northwest-Corner RuleThe Intuitive Lowest-Cost MethodTHE STEPPING-STONE METHODSPECIAL ISSUES IN MODELINGDemand Not Equal to SupplyDegeneracy2Learning ObjectivesWhen you complete this chapter, you should be able to :Identify or Define:Transportation modelingFacility location analysisExplain or be able to use:Northwest-corner ruleStepping-stone method3Transportation ProblemDesMoines(100 unit capacity)Fort Lauderdale(300 units capacity)Cleveland(200 units required)Evansville(300 units capacity)Albuquerque(300 units required)Boston(200 units required)4How much should be shipped from several sources to several destinations Sources: Factories, warehouses, etc.Destinations: Warehouses, stores, etc.Transportation modelsFind lowest cost shipping arrangementUsed primarily for existing distribution systemsTransportation Problem5A Transportation Model RequiresThe origin points, and the capacity or supply per period at eachThe destination points and the demand per period at eachThe cost of shipping one unit from each origin to each destination622nSupply Quantity SourceQuantity ShippedDestinationaiixmnjbja11b1x11a2x22b2::x2n::amxmnbnx1nx12x21Demand Quantity mxm21xm1Transportation ProblemGraphical Solution7Define problemSet up transportation table (matrix)Summarizes all dataKeeps track of computationsDevelop initial solutionNorthwest corner ruleFind optimal solutionStepping stone methodTransportation ProblemSolution Steps8Transportation CostsFromTo(Destination)(Sources)AlbuquerqueBostonClevelandDes Moines$5$4$3Evansville$8$4$3FortLauderdale$9$7$59Transportation TableDestinationSourceSupplyDemand12:ma1a2:am12. .nb1b2bnQuantity demanded or required10Transportation TableDestinationSource12. .nSupply1x11c11x12c12. .x1nc1na12x21c21x22c22. .x2nc2na2::::::::::mxm1cm1xm2cm2. .xmncmnamDemandb1b2. .bnCost of supplying 1 unit from sources to destinations11Transportation TableDestinationSourceSupplyDemand12:ma1a2:am12. .nb1b2bnx11x12. .x1nx21x22. .2n:::::::xm1xm2. .xmn:xQuantity supplied from sources to destinations12Transportation TableToFromAlbuquerque(A)Boston(B)Cleveland(C)FactoryCapacityDes Moines(D)100Evansville(E)300Fort Lauderdale(F)300WarehouseRequirements30020020070058974433513Initial Solution Using the Northwest Corner RuleToFromAlbuquerque(A)Boston(B)Cleveland(C)FactoryCapacityDes Moines(D)100100Evansville(E)200100300Fort Lauderdale(F)100200300WarehouseRequirements30020020070058974433514The Stepping Stone MethodSelect any unused square to evaluateBegin at this square. Trace a closed path back to the original square via squares that are currently being used (only horizontal or vertical moves allowed)Place + in unused square; alternate - and + on each corner square of the closed pathCalculate improvement index: add together the unit cost figures found in each square containing a +; subtract the unit cost figure in each square containing a -.Repeat steps 1-4 for each unused square15Stepping-Stone Method: Tracing a Closed Path - Des Moines to ClevelandToFromAlbuquerque(A)Boston(B)Cleveland(C)FactoryCapacityDes Moines(D)100100Evansville(E)200 100300Fort Lauderdale(F) 100200300WarehouseRequirements300200200700589744335Start+++---16The Intuitive Lowest Cost MethodIdentify the cell with the lowest cost. Arbitrarily break any ties for the lowest cost.Allocate as many units as possible to that cell without exceeding the supply or demand. Then cross out that row or column (or both) that is exhausted by this assignment.Find the cell with the lowest cost from the remaining cells.Repeat steps 2 & 3 until all units have been allocated.17ToFromAlbuquerque(A)Boston(B)Cleveland(C)FactoryCapacityDes Moines(D)100100Evansville(E)200100300Fort Lauderdale(F)300300WarehouseRequirements300200200700589744335First, cross out top rowSecond, cross out column CThird, cross out row EInitial Solution Using the Intuitive Lowest-Cost Method18Linear programming model is difficult to formulate & solveSpecial purpose methodsAre easier to formulateAre faster to computeGive integer solutionsMethodsStepping-stoneMODISee your CD Tutorial © 1995 Corel Corp.Specialized Methods19Demand not equal to supplyCalled ‘unbalanced’ problemAdd dummy source if demand > supplyAdd dummy destination if supply > demandDegeneracy in Stepping Stone MethodToo few shipping routes (cells) usedNumber of occupied cells should be: m + n - 1Create artificially occupied cell (0 value)Represents fake shipmentSpecial Issues in the Transportation Model20Transportation TableDemand Not Equal SupplyToFromAlbuquerque(A)Boston(B)Cleveland(C)FactoryCapacityDes Moines(D)250Evansville(E)300Fort Lauderdale(F)300WarehouseRequirements300200200700589744335000Dummy150New Des Moines capacity21DegeneracyToFromAlbuquerque(A)Boston(B)Cleveland(C)FactoryCapacityDes Moines(D)100100Evansville(E)200100300Fort Lauderdale(F)200200WarehouseRequirements30010020070058974433522Degeneracy - ContinuedToFromAlbuquerque(A)Boston(B)Cleveland(C)FactoryCapacityDes Moines(D)100100Evansville(E)200100300Fort Lauderdale(F)200200WarehouseRequirements300100200700589744335023